# 9 15 (KnotPlot image) See the full Rolfsen Knot Table. Visit 9 15's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9 15 at Knotilus!

### Knot presentations

 Planar diagram presentation X1425 X7,10,8,11 X3948 X9,3,10,2 X13,17,14,16 X5,15,6,14 X15,7,16,6 X11,1,12,18 X17,13,18,12 Gauss code -1, 4, -3, 1, -6, 7, -2, 3, -4, 2, -8, 9, -5, 6, -7, 5, -9, 8 Dowker-Thistlethwaite code 4 8 14 10 2 18 16 6 12 Conway Notation 

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 2 Bridge index 2 Super bridge index $\{4,5\}$ Nakanishi index 1 Maximal Thurston-Bennequin number [-1][-10] Hyperbolic Volume 9.8855 A-Polynomial See Data:9 15/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $2$ Rasmussen s-Invariant 2

### Polynomial invariants

 Alexander polynomial $-2 t^2+10 t-15+10 t^{-1} -2 t^{-2}$ Conway polynomial $-2 z^4+2 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 39, 2 } Jones polynomial $-q^8+2 q^7-4 q^6+6 q^5-6 q^4+7 q^3-6 q^2+4 q-2+ q^{-1}$ HOMFLY-PT polynomial (db, data sources) $-z^4 a^{-2} -z^4 a^{-4} -z^2 a^{-2} +2 z^2 a^{-6} +z^2- a^{-2} + a^{-4} + a^{-6} - a^{-8} +1$ Kauffman polynomial (db, data sources) $z^8 a^{-4} +z^8 a^{-6} +2 z^7 a^{-3} +4 z^7 a^{-5} +2 z^7 a^{-7} +2 z^6 a^{-2} +z^6 a^{-4} +z^6 a^{-6} +2 z^6 a^{-8} +2 z^5 a^{-1} -z^5 a^{-3} -7 z^5 a^{-5} -3 z^5 a^{-7} +z^5 a^{-9} -4 z^4 a^{-6} -5 z^4 a^{-8} +z^4-3 z^3 a^{-1} +5 z^3 a^{-5} -z^3 a^{-7} -3 z^3 a^{-9} -3 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2 a^{-6} +3 z^2 a^{-8} -2 z^2+z a^{-1} +z a^{-3} -z a^{-5} +z a^{-7} +2 z a^{-9} + a^{-2} + a^{-4} - a^{-6} - a^{-8} +1$ The A2 invariant $q^4+2 q^{-2} -2 q^{-4} +2 q^{-12} +2 q^{-16} - q^{-20} + q^{-22} - q^{-24} - q^{-26}$ The G2 invariant $q^{18}-q^{16}+3 q^{14}-3 q^{12}+2 q^{10}-3 q^6+8 q^4-9 q^2+11-9 q^{-2} +5 q^{-4} +4 q^{-6} -13 q^{-8} +23 q^{-10} -26 q^{-12} +21 q^{-14} -13 q^{-16} -5 q^{-18} +20 q^{-20} -31 q^{-22} +33 q^{-24} -20 q^{-26} +2 q^{-28} +14 q^{-30} -23 q^{-32} +15 q^{-34} -2 q^{-36} -13 q^{-38} +24 q^{-40} -23 q^{-42} +9 q^{-44} +17 q^{-46} -34 q^{-48} +46 q^{-50} -42 q^{-52} +21 q^{-54} +6 q^{-56} -28 q^{-58} +43 q^{-60} -44 q^{-62} +36 q^{-64} -11 q^{-66} -11 q^{-68} +26 q^{-70} -30 q^{-72} +20 q^{-74} - q^{-76} -15 q^{-78} +21 q^{-80} -15 q^{-82} +3 q^{-84} +18 q^{-86} -31 q^{-88} +33 q^{-90} -23 q^{-92} +18 q^{-96} -32 q^{-98} +33 q^{-100} -24 q^{-102} +10 q^{-104} +3 q^{-106} -15 q^{-108} +17 q^{-110} -15 q^{-112} +9 q^{-114} -3 q^{-116} -2 q^{-118} +3 q^{-120} -4 q^{-122} +3 q^{-124} - q^{-126} + q^{-128}$